In the war between the United States and terrorists since the 1983 bombing of the American Embassy in Beirut, Lebanon, the score is grim.

Today it stands: Americans killed in bombings and hijackings in the Middle East and Africa -- 307. Terrorists convicted for those crimes by American courts -- a bare handful.

As the Federal Bureau of Investigation and the Central Intelligence Agency set up shop in borrowed offices here and in Tanzania, scrounging desks and telephones while spearheading a global search for the people who bombed the American embassies five days ago, they know all too well that acts of terror committed overseas are the most difficult cases to crack.

The complexity and sophistication of foreign terrorist organizations is increasing, present and former intelligence officials say. The audacious timing and logistical skill required in the bombings last week -- one group fomenting two nearly simultaneous attacks more than 300 miles apart, killing at least 257 people and leaving no clear trace -- was breathtaking to veterans of the war on terrorism.

''Two at once is not twice as hard,'' said Milton Bearden, a retired senior C.I.A. official who was the ranking officer for the agency in Afghanistan, Pakistan and the Sudan. ''Two at once is 100 times as hard.''

The war was hard enough before the bombings. Terrorist groups seem to know more about American intelligence than American intelligence knows about them, Mr. Bearden said.

The F.B.I., the domestic law-enforcement agency, is operating abroad, searching for clues in unfamiliar terrain and seeking help from local officials and other residents who are sometimes unhelpful.

On overseas investigations, the two agencies have to work together. But they began only recently to cooperate, after decades of mutual mistrust, intelligence and law-enforcement veterans say.

The Kenyan Government announced tonight that it had arrested suspects. So did the Government in Tanzania this week. But those arrests appear unpromising. And there are many reasons not to expect swift justice under American law. The intelligence agency, despite its best efforts, has few reliable sources in international terrorist networks.

No one may ever know whether the bombings last week were supported by a state like Iraq, an intelligence service like Iran's or an individual like the exiled Saudi financier Osama Bin Laden. Mr. Bin Laden has hailed such attacks in the past, financed terrorist groups from Egypt to Algeria to Afghanistan and sought to unify them under his banner, intelligence officials say.

''This in all likelihood was not state supported, and if it's not, 'Terror Inc.' is beginning to creep in,'' Mr. Bearden said. ''Whether or not Bin Laden was in on it there may be an emerging linkage between Bin Laden, the Islamic Jihad guys and the Islamic Group out of Egypt. If so, these people are close to becoming a state unto themselves.''

All are suspects, American officials said. But following a trail from the rubble of the embassies to a command center in Baghdad, a clandestine cell in Teheran or a terrorist training camp in Afghanistan would be a long haul.

The networks are by nature almost impossible to unravel. The chain of command in a sophisticated group connects the intellectual author of the terror to the attackers who carry out his will. But that chain has many links, and no one person in the chain may know the identity of the next.

The man who builds the bomb may know nothing of the man who pays him, or the man who drives the bomb to its target. So locating a bomber or his car may lead nowhere.

The search sometimes never ends. The C.I.A. is still looking for the assassins who killed its Athens station chief, Richard Welch, in 1975. And no one has ever been arrested by American authorities in the bombings of the United States Embassy and the Marine barracks in Beirut in 1983 that killed 255 people, or in the bombings of two military posts in Riyadh and Dhahran, Saudi Arabia, in 1995 and 1996 that killed two dozen American military personnel.

But the Beirut and Dhahran cases provide lessons for the investigators in Nairobi and Dar es Salaam today. The investigation of the Dhahran bombing, which killed 19 airmen, is at a dead end. The F.B.I. and the Saudi intelligence service would not share information. The bureau, which had never conducted an investigation in the kingdom, said the Saudis were uncooperative. The Saudis said the bureau was highhanded.

''You can never catch the bad guys without the help of your friendly local foreign security and intelligence services,'' Mr. Bearden said. ''You can't run roughshod over them.''

The hunch that the Dhahran bombing was carried out by Saudi dissidents with the help of outsiders -- possibly Iran or Mr. Bin Laden -- remains unproven. Suspicions that Iran has had a hidden hand in such bombings date from the start of the modern era of terrorism against American diplomatic and military posts, the bombing of the Beirut Embassy in April 1983.

That explosion damaged the C.I.A.'s ability to understand, infiltrate and nullify Islamic terrorism. The bomb destroyed the agency's Beirut station, killing seven officers, among them Robert Ames, the top Mideast analyst. He had been the chief of the clandestine service in the Arab world and a covert agent in Iran, Lebanon, Kuwait and Yemen.

Ten years before the bombing, he had won the trust of Ali Hassan Salemeh, the security chief of Al Fatah, then one of the most feared terrorist organizations. Mr. Salemeh provided the agency with warning of the assassination plots of radical Palestinian groups and helped the agency obtain agents in Islamic political and guerrilla organizations, former intelligence officials said. In 1979, Mr. Salemeh was killed by a car bomb, probably by the Mossad Israel's intelligence service.

The agency has never had a source quite like Mr. Salemeh or an officer quite like Mr. Ames, some intelligence officials said. The lesson, they added, is that an intelligence service is only as good as its spies and its sources. Until recently, another problem in terrorist investigations outside the United States was a deep friction between the Central Intelligence Agency and the Federal Bureau of Investigation.

''The C.I.A. and the F.B.I. did not cooperate as well as they ought to,'' Jeffrey Smith, a former general counsel at the intelligence agency, said. ''They did not share information. They frankly were suspicious of each other.''

In 1996, Mr. Smith said, the bureau and the agency confronted the fact that they were like the Army and the Navy during the invasion of Grenada. He used the image that they could not communicate because their radios operated on different frequencies.

They came from different cultures. A law-enforcement officer who is confronting an evildoer wants to string him up. An intelligence officer wants to string him along, to find out what he knows.

To overcome that clash, ''we got senior C.I.A. people from Europe and the Middle East together with senior people from the F.B.I.'' for a three-day meeting two years ago in Rome, Mr. Smith said. ''They asked each other, 'How do you handle the joint takedown of the terrorist organization? Do you do this for purposes of prosecution or for purposes of penetration?' It was the first time these conversations had occurred, and when it was over the deputy director of the F.B.I. said, 'We should have done this 40 years ago.' ''

The double bombing is not just the biggest joint counterterrorism investigation mounted overseas by American intelligence and law-enforcement agencies. It is the first in which they share rules and roles. Still, they will need more than smooth coordination to solve the case.

Some Federal investigators who arrived here 36 hours after the explosion said the sight reminded them of the bombed-out Federal building in Oklahoma City, where they worked in 1995. But whoever bombed the embassies was a good deal more professional than Timothy J. McVeigh, the Army veteran who carried out the Oklahoma City attack and whose idea of a smooth getaway was to speed down a state highway without license plates.